Doncaster has vowed to help the police track down those responsible for wrecking almost 200 seats.
A reported £10,000 worth of damage was caused to seats in the lower section of the south stand housing away fans - just above where a Green Brigade banner was displayed - during the 5-0 romp for Neil Lennon's men against Motherwell.
Celtic have now made moves to disband the ultras' section at Parkhead after labelling the incident "indefensible".
And SPFL chief Doncaster has confirmed the league body will take action against Celtic, with disciplinary proceedings expected to open by the end of the week.
Under SPFL rule H40, if found guilty, Celtic will be ordered to pay for the damage.
Doncaster said: "We have already been in touch with both clubs and the police following the disturbances during Friday night's fixture at Fir Park. We absolutely condemn this type of behaviour - it has no place in the game.
"We are confident that the police and both clubs will play a full part in helping to identify those involved in what were shameful scenes.
"We expect the SPFL Match Delegate report to be with us within the next 24-48 hours.
"The SPFL will work closely with our colleagues at both clubs and with the police as part of a thorough investigation into Friday night's events."
Friday's trouble started when a flare was let off in the area behind Fraser Forster's goal before the game while two green smoke bombs were thrown into the goalmouth, one of them landing yards from the Hoops keeper.
Now the club have handed "precautionary suspensions" to 128 supporters preventing them from attending home and away matches, while 250 season-ticket holders housed in section 111 - the Green Brigade's corner of Celtic Park - will be moved to other parts of the ground.
A Celtic spokesman said: "Events such as those on Friday night do not represent the Celtic support or the club. These events were an embarrassment to our great football club and are absolutely indefensible."